It is known that optical waveguides can be produced on glass plates made of sodium silicate glass, with Na.sup.+ ions in the glass being replaced by Ag.sup.+ ions from a silver bath. The areas of the substrate where the exchange is to take place are usually defined by patterned covering of the surface areas of the substrate not intended for exchange by photoresist masks or copy resist masks in patterns obtained by exposing and washing or developing the photoresist layer. After treatment in a silver bath, which only has access to the exposed surface areas of the substrate, the refractive index in these areas is increased in comparison with the surrounding glass. This yields an optical waveguide, with the evanescent wave being located completely in the thick substrate glass. It would be desirable in principle to produce optical waveguides in silicon dioxide layers instead of glass, because this would offer the possibility of combining them with semiconductor elements. However, this is made difficult by the fact that thick silicon dioxide layers cannot be produced in an adequate optical quality; a high-grade thermally produced oxide can be manufactured industrially only up to a thickness of a few .mu.m. This would not be sufficient for the evanescent light field. Furthermore, the oxide cannot be doped completely homogeneously with sodium ions, which would be necessary for an exchange reaction.